Definition of double-suited
Double-suited means cards that are "double-suited". The term is mostly used in Omaha. In Hold'em, when you receive AK in spades preflop, you are said to have suited cards. The term is also used in Omaha for matching cards. And since you are dealt 4 cards in Omaha, you may be dealt AK in spades and AK in hearts, for example. This is called a "double-suited" hand. Regardless of the combination, if you receive two cards of one suit and two cards of another suit, you have a double-suited hand.
Suited vs double-suited in Omaha and equity
Unlike Hold'em where it's good news to receive cards that are both the same suit, in Omaha it's bad news. If you receive four cards in spades or four cards in hearts in Omaha, it's bad news because you know you're less likely to hit your flush. However, if you have a double-suited hand, it's good news. The fact that your hand is double-suited will add equity. For example, if you have a hand like 5-6-7-8 unmatched, you will have 42% equity against a random hand. But if you have 5-6-7-8 double-suited, you will now have 49% equity against a random hand.